yr1 chap 4 graphs + transformations

• y = f(x+a) is a translation in the x direction

  x coordinate: subtract a

  y coordinate: no change
• y = f(x) + a is a translation in the y direction

  x coordinate: no change

  y coordinate: add a
• y = f(ax) is a stretch in the x direction, the scale factor is 1/a

  x coordinate: divide by a

  y coordinate: no change
• y = af(x) is a stretch in the y direction, the scale factor is a

  x coordinate: no change

  y coordinate: multiply by a
• y = f(-x) is a reflection in the y axis

  x coordinate: change sign

  y coordinate: no change
• y = -f(x) is a reflection in the x axis

  x coordinate: no change

  y coordinate: change sign
• with transformations except reflections, if the change is outside the bracket it affects the y coordinate in the way you would expect, and if the change is inside the bracket it affects the x coordinate in the opposite way to what you would expect
• y = (ax + b) is a translation by -b then a stretch by 1/a, you need to do it in this order not the reverse to get the correct graph